Bead on a wavy wire

Classical Mechanics Level 3

A bead slides down on a frictionless wire, starting from rest at point A. The section from A to B is straight while the section from B to C is wavy (with wavelength \(\lambda\ll L\)). The total length of the stretched wire is \(3L\). If \(L=50~\text{cm}\), determine the time in seconds it takes for the bead to reach point C. Assume that the bead slides smoothly at all times.